Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If b is directly proportional to a the equation is of the form b = ka (where k is a constant). Two variables are said to be in direct variation when the variables are related in such a way that the ratio of their values always remains the same. Direct variation is expressed in various mathematical forms. In equation form, y and x vary directly since the ratio of y to x never changes.
The Direct Variation Formula is,
\[\LARGE y=kx\]
Solved Example
Question: The quantity of wooden box made is directly proportional to the number of wooden blocks. The number of wooden blocks needed for 30 boxes is 120. How much wooden blocks are needed for a box?
Solution:
Solution:
In the given problem,
Number of wooden blocks needed for 30 boxes = y = 120
Number of boxes = x = 30
Number of wooden blocks needed for a box = k
The direct variation formula is,
y = k * x
120 = k * 30
Number of wooden blocks needed for 30 boxes = y = 120
Number of boxes = x = 30
Number of wooden blocks needed for a box = k
The direct variation formula is,
y = k * x
120 = k * 30
k = 120/30
k =Â 4
Number of wooden blocks needed for a box =Â 4
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